Rare decayπ0→e+e−: Theory confronts KTeV data

Abstract

Within the dispersive approach to the amplitude of the rare decay ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}$ the nontrivial dynamics is contained only in the subtraction constant. We express this constant, in the leading order in $({m}_{e}/\ensuremath{\Lambda}{)}^{2}$ perturbative series, in terms of the inverse moment of the pion transition form factor given in symmetric kinematics. By using the CELLO and CLEO data on the pion transition form factor given in asymmetric kinematics, the lower bound of the decay branching ratio is found. The restrictions following from QCD allow us to make a quantitative prediction for the branching $B({\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}})=(6.2\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\cdot\else\textperiodcentered\fi{}{10}^{\ensuremath{-}8}$ which is $3\ensuremath{\sigma}$ below the recent KTeV measurement. We confirm our prediction by using the quark models and phenomenological approaches based on the vector meson dominance. The decays $\ensuremath{\eta}\ensuremath{\rightarrow}{l}^{+}{l}^{\ensuremath{-}}$ are also discussed.